MinT - Information on Result #940368

Information on Result #940368

Linear OOA(8¹¹⁶, 374, F₈, 2, 40) (dual of [(374, 2), 632, 41]-NRT-code), using trace code based on linear OOA(64⁵⁸, 187, F₆₄, 2, 40) (dual of [(187, 2), 316, 41]-NRT-code), using

constructionÂ X applied to AG(2;F,311P) âŠ‚ AG(2;F,323P) [i] based on
1. linear OOA(64⁴⁷, 176, F₆₄, 2, 40) (dual of [(176, 2), 305, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,311P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(64³⁵, 176, F₆₄, 2, 28) (dual of [(176, 2), 317, 29]-NRT-code), using algebraic-geometric NRT-code AG(2;F,323P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64¹¹, 11, F₆₄, 2, 11) (dual of [(11, 2), 11, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹¹, 64, F₆₄, 2, 11) (dual of [(64, 2), 117, 12]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;117,64) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹¹⁶, 187, F₈, 3, 40) (dual of [(187, 3), 445, 41]-NRT-code)	[i]		OOA Folding